There are two test centers at FRA, Centogene and EcoCare. I personally know that Centogene is behind the customs gate and EcoCare is in Terminal 1/2. Have you tried calling EcoCare? They have a phone number and email address at their website https://flughafen-frankfurt.ecocare.center/en/
Telephone: +49 211 387 895 73
In Zürich the airside testing centre is at the transit hotel, that is connected to concourse D, which is Non-Schengen. So you do not need to enter the country to get there.
The only wrinkle is that if your flights are from concourse E that you will have to pass through security each time. ZRH does not have a clean path from D to E, so you always need to go ...